analysis (differential/integral calculus, functional analysis, topology)
metric space, normed vector space
open ball, open subset, neighbourhood
convergence, limit of a sequence
compactness, sequential compactness
continuous metric space valued function on compact metric space is uniformly continuous
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In real analysis, the reciprocal is a partial function implicitly defined over the non-zero real numbers by the equation . This is the definition commonly used when defining the real numbers as a field.
The reciprocal is piecewise defined as
This definition implies that the reciprocal is analytic in each of the two connected components of the domain.
Let us define the functions and from the open subinterval of the real numbers to the real numbers as the locally convergent power series
The reciprocal is then piecewise defined as
Equivalently, given an element , the reciprocal is then piecewise defined as
This definition implies that the reciprocal is analytic in each of the two connected components of the domain.
Last revised on December 4, 2022 at 21:58:18. See the history of this page for a list of all contributions to it.